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# lecture7 - Definitions Ambiguity and vagueness in ordinary...

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Definitions Ambiguity and vagueness in ordinary language can impede clear thinking and reasoning, and lends to some problems in logic. A word is ambiguous if it has more than one meaning. e.g. ‘bank’ can mean ‘financial institution’ and ‘river bank’. A word is vague if it admits of borderline cases : cases in which it neither clearly applies nor clearly does not apply. e.g. ‘bald’, ‘rich’, ‘mountain’, ‘person’.

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Problems with vagueness In fact, vagueness (in this technical sense) leads to notorious paradoxes. 1) Homer Simpson has two hairs on his head and is bald 2) If HS has n hairs on his head and is bald, then if HS had n+1 hairs on his head, HS is bald. So, 3) If HS has 3 hairs on his head then he is bald. But given (2) and (3), 4) If HS has 4 hairs on his head then he is bald. And we can repeat this line of reasoning as many times as we like. So we’ll end up with: If HS has 100,000,000 hairs on his head then he is bald. But this is obviously false.
Definitions Clarity about the meanings of our terms helps to clear up some of this ambiguity and vagueness. This is where definitions come in. Definitions give the meaning of a word or phrase (term). But there are different ways of doing this and so different types of definition. Two ways of defining a term: (1) Give its extension : the set of things to which it applies. (2) Give its intension : the properties a thing must have to be included in the term’s extension. Ex. the extension of ‘Phil 3 TA’ is: Jon and Dan . the intension is something like: person who holds Phil 3 sections, grades work, etc

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Extensional definitions Two types of extensional definition: (1) Ostensive definition: that’s a graduate student; that’s a table, that’s the ocean, etc. (2) Verbal definition: ‘Baltic state’ means Estonia, Latvia or
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lecture7 - Definitions Ambiguity and vagueness in ordinary...

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